Responding to a fellow user of Twitter who described Page 3 as "so last century", News Corp's chairman and chief executive said that he was "considering" whether he was of the same view.

Murdoch, whose tweets are closely scrutinised for clues to the future direction of his global media empire, commented: "page three so last century! You maybe right, don't know but considering. Perhaps halfway house with glamorous fashionistas."

A News International spokesperson said the company was making no comment in relation to whether the Sun's topless Page 3 could be for the axe.

Suspicion that the upper echelons of News International could have reached a tipping point was fuelled by another tweet from a lifelong Murdoch confidant who was asked what he made of Murdoch's comment.

In the most recent campaign against Page 3, supermarkets across Britain have been targeted by activists as they stepped up their campaign for an advertising boycott of the tabloid.

Members of the campaign group No More Page 3 said it was a sexist relic of an unhealthy 1970s culture that was at odds with the family values promoted by supermarkets.

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The campaign, which has attracted more than 64,310 signatures of support on a change.org petition, posted a video on YouTube of interviews about Page 3 with male Sun readers, many of whom said it was degrading and sexist. The group has also held weekly protests outside News International.

Beyond activist circles, the view that Page 3 has had its day has been gaining ground for some time. Ross Brown, a former editor of FHM magazine, said last year : "One of my best friends is the editor of Nuts and we spend much of our time arguing. I think it's just reached a point where it's readily accessible porn, from Page 3 to Nuts. And we're past that."

According to Fleet Street lore, Murdoch is said to have been unhappy when topless Page 3s were introduced by the then Sun editor Larry Lamb in November 1970. However, any latent opposition the proprietor harboured at the time appears to have vanished as the newspaper's circulation rose and the topless Page 3s become closely associated with the brand.

In 1986, Clare Short raised the issue in the House of Commons, leading to supportive letters from women and attacks by the paper.

Forced to give evidence for the second time after the inquiry heard criticisms of the newspaper from a coalition of women's groups, Mohan insisted that Page 3 of the Sun was an innocent staple of British life and its daily pictures of topless models celebrate natural beauty.

• This article was amended on 11 February 2013 to include the full Twitter response from former News International chairman Les Hinton to a question about Rupert Murdoch's tweet.